Midi, UDP, OSC communication of the two computers eg. You could even use a digital audio signal for high precision over adat or SPDIF. (I guess there shouldn't be any digital DC filtering on neither in nor output of these)

I don't have much trouble getting the two computers to communicate using one of the protocols you listed, but I am having trouble having the second computer understand where the first computer's current location in the buffer is, and having the second computer pick up and play alongside the first.

hm. depends what exactly you are trying to achieve but what about sending the current playing position in ms via OSC and having the second computer start from there? Or I don't understand your problem. Could you be more specific?

Do you think it is possible to send a continuous line~ message through osc that could coordinate two devices to a buffer position?